The present invention relates to a measurement method arid measurement apparatus employing an interferometer arranged to form patterns of interference fringes.
Interferometers are well-known, and the testing and measurement of: optical components, from simple spectacle lenses to astronomical telescopes requires an interferometer system of one sort or another. Interferometers are also now routinely applied in engineering for the measurement of mechanical and thermal behaviour of materials and components.
Conventionally, for the most accurate measurement these interferometer systems are constructed from high-quality optical elements and include fine controls for precise alignment. The need for high quality, precise components makes interferometer systems expensive and places practical restrictions on the aperture of the instrument. Typically, the controls are adjusted to reduce the number of interference fringes formed in the observer""s field of view before the test or measurement is performed to a minimum, and ideally zero. Then, an object to be tested is inserted in one arm of the interferometer, or the interferometer is perturbed (altered) in some other way. If the interferometer was initially set up to produce a fringe-free field, then all interference fringes appearing in the test interferogram are due to the perturbation.
In conventional interferometer measurement applications, a few fringes in the initial (i.e. reference) interferogram may be tolerated, if the test/measurement perturbation results in an interference pattern having a large number of fringes. The underlying imperfections in the unperturbed interferometer may be ignored.
If, however, the test/measurement perturbation itself only introduces a small number of fringes, then the underlying imperfections cannot simply be ignored.
Techniques are known for removing the effects of aberrations in the reference interferogram so as to display an image from a test component which is free from spurious fringes generated by an imperfect optical system. The method for applying the correction is, however, both elaborate and slow. From one or more interferograms of the reference and test object he phase distributions are calculated. The method typically necessitates the conversion of at least three test interference fringe patterns (interferograms) and at least three reference interferograms into digital images to facilitate processing. The three or more reference and test interferograms are phase stepped (shifted) from each other by pre-determined amounts. These phase shifted patterns are generated sequentially by the appropriate phase shifting of fringes, for example by a piezoelectric transducer-(PZT)-driven mirror or wavelength modulation.
Once the phase distributions (phase maps) have been calculated an unwrapping procedure is then applied to the phase maps. As the test phase maps also contain the reference information, subtraction of the reference map from the test map results in the presentation of the test information only. As a consequence or the delay, the subtraction is usually performed off-line and post-operatively. In addition, the approach may fail because the phase calculation and unwrapping procedures will not tolerate interferograms with excessive numbers of closely spaced fringes or fringes which are contorted.
It is also known to derive an accurate phase map of the optical path perturbation resulting from a test component by deliberately introducing carrier fringes (a spatial carrier) into the test interferogram by, for example, tilting a mirror in the interferometer, and performing a Fourier transform analysis method. Rather than requiring a least three reference interferograms, with the Fourier transform method only one fringe pattern having a spatial carrier is enough for the analysis. However, it requires more computation for Fourier transformation and filtering and cannot be conducted in real-time. Therefore it has not been easy to accelerate fringe analysis for quick applications such as feedback control of optical instruments and real-time monitoring of dynamic phenomena.
The paper xe2x80x9cVideo-rate fringe analyzer based on phase-shifting electronic moirxc3xa9 patternsxe2x80x9d, Kato et al, Applied Optics, Nov. 10, 1997, Vol. 36, No. 32, p8403xe2x80x94describes a fringe analyzer that delivers the phase distribution at a video-rate from a fringe pattern containing a spatial carrier. It is based on parallel generations of three phase-shifted moirxc3xa9 patterns through electronic multiplication with computer-generated reference gratings and low-pass filtering. The phase distribution is derived by the subsequent parallel processing of these patterns on the basis of a three-step phase-shifting algorithm.
Image processing involving digital subtraction of images is known in digital speckle pattern interferometry (described, for example, in xe2x80x9cSpeckle Metrologyxe2x80x9d, Ed. R. S. Sirohi, Marcel Deker, Inc. New York, 1993, p125) and in document analysis (described, for example, in xe2x80x9cA new method for displaying indented and other markings on documentsxe2x80x9d, C. Forno, Science and Justice 1995, 35 (1) 45-51), and in xe2x80x9cMore technique by means of digital image processingxe2x80x9d, K. J. Gasvick, Applied Optics 1983, 22 (23) 3543-8.
Moirxc3xa9 fringe generation is a known process whereby the intensity distributions of two dissimilar grid patterns are combined, for example by superimposition, as described in Chapter 6, xe2x80x9cHandbook of Experimental Mechanicsxe2x80x9d, Society for Experimental Mechanics Inc, Prentice Hall, Englewood Cliffs, N.J. 07632, USA 1987, ISBN:0-3-377706-5. By superimposing the dissimilar grids, a moirxc3xa9 fringe pattern is generated which represents the local differences between the spatial frequencies of the grids.
According to a first aspect of the present invention, there is provided a measurement method comprising the steps of:
arranging an interferometer to form a first interference fringe pattern comprising at least ten interference fringes;
recording an image of said first interference fringe pattern;
perturbing an optical path in the interferometer to form a second interference fringe pattern comprising at least ten interference fringes; and
combining an image of said second interference fringe pattern with the recorded image of the first interference fringe pattern to produce a further image comprising a moirxc3xa9 fringe pattern arising from a difference or differences between the first and second interference fringe patterns.
Thus, it is no longer necessary to align the interferometer with great precision to produce a substantially fringe free reference (i.e. first) interference fringe pattern before the test or measurement is performed (i.e. before the interferometer is perturbed/altered).
The moirxc3xa9 fringe pattern produced by combining the first and second interference fringe patterns is determined by the perturbation itself, and not by the underlying Imperfections and misalignments of the unperturbed interferometer.
In this new approach, all the errors of a poor quality, misaligned system are accepted and then eliminated by the combination process, producing a moirxc3xa9 fringe pattern. The method enables very large aperture optical systems for traditional and engineering interferometers to be constructed from inexpensive and basic components.
A conventional high quality optical measurement interferometer will typically comprise optical components having surfaces manufactured to tolerances of better than xcex/10 or even xcex/100 where xcex is the wavelength of light input to the interferometer.
With the inventive method, imperfections in optical components as large as 100xcex or greater may be tolerated.
The interferometer used in the present invention may be an optical interferometer, or alternatively may be an interferometer arranged to form an interference pattern from incident electromagnetic radiation having different wavelength.
In a basic form, the method may be implemented by recording the first image on, for example, a photographic film. The subsequent interference fringe pattern, produced by perturbing the interferometer system, may then be projected onto the recorded image and the resultant moirxc3xa9 fringe pattern observed.
Alternatively, the recorded image may be captured by a camera, such as a high resolution electronic camera where the image of the interference pattern is focussed onto a CCD (Charge Coupled Device) sensing element.
The images combined to produce the moirxc3xa9 fringe pattern may be digital images, facilitating the processing and enabling a variety of combination procedures to be employed, for example subtraction, multiplication, addition, and/or superimposition.
Thus, the combining step may comprise one or more of the steps of adding, subtracting, filtering, superimposing, or multiplying the images.
Advantageously the images of the first and second interference fringe patterns may be combined by a process of digital subtraction.
In order to produce moirxc3xa9 fringe patterns, each of the first and second interference fringe patterns clearly needs to comprise a number of fringes. Ten is a practical lower limit, but better (i.e. more detailed) moirxc3xa9 fringe patterns may be obtained by increasing the number of fringes in the first and second patterns.
Advantageously, the method may therefore include the step of tilting a reflecting surface of the interferometer to increase the number of interference fringes.
If the components of the interferometer are sufficiently irregular, or the alignment is already sufficiently poor, however, then no further adjustment may be needed to provide an interference fringe pattern comprising a large number of fringes.
Advantageously, the first interference fringe pattern may comprise at least fifty, and preferably at least 100 fringes.
Preferably, the spatial frequency of the fringes in the first (reference) interference pattern should be higher than the spatial frequency of fringes that would be introduced by the measurement/test perturbation, were the interferometer set up to produce an initial fringe-free field, i.e. the carrier fringe spatial frequency should be higher than the spatial frequency of the phase distribution to be measured.
The number of fringes in the first interference fringe pattern may be larger than, smaller-than, or the same as the number in the second pattern.
The perturbation may result in the second interference fringe pattern having fewer fringes than the first pattern, but ideally the interferometer should be arranged so that the number of fringes in the interference fringe pattern produced by the interferometer is increased by the perturbation, i.e. the second pattern comprises more fringes than the first. For example, a detailed moirxc3xa9 fringe pattern may be produced by combining a first image of 100 fringes with a second image of 150 fringes.
The perturbation to the interferometer system may take a number of forms. For example, the step of perturbing may comprise the step or inserting a transparent test object in the optical path (e.g. inserting the object in one arm of the interferometer).
The step of perturbing may comprise the distortion, rotation, and/or translation of a reflecting surface or a transparent object in the optical path.
The step of perturbing may comprise the step of replacing a reference object with a test object, and the first interference fringe pattern may have been recorded with the reference object in place.
The step of perturbing may alternatively, or in addition, comprise the step of disturbing a gas and/or disturbing the flow of a gas in the optical path.
The image of the second interference fringe pattern may also be a recorded image, or alternatively may be a live image output by a camera.
Advantageously one or both of the recorded image of the first interference fringe pattern and the image of the second interference fringe pattern may be images selected from a recorded sequence of images of the interference fringe pattern formed by the interferometer.
Advantageously the recorded image of the first interference fringe pattern and the image of the second interference fringe pattern may be digital images.
Preferably, the step of combining includes the step of subtracting one of the digital images from the other. Advantageously, with modern image processing software, the subtraction computation is trivial and can be performed, and the result (the further image) displayed almost continuously in real time.
Thus, by applying the principles of moirxc3xa9 in digital form to interferometry, optical aberrations can be made inconspicuous and apart from the time required to perform a simple image subtraction between reference and object images, there are no other delays in presenting the corrected interferogram. In addition, the method can better accommodate gross aberrations, thus offering the opportunity of constructing systems from inexpensive components of poor optical quality. There is no need to align the interferometer precisely and so an economy can be made on the quality of the mechanical adjustments. Advantageously, the step of combining may include the step of converting negative values obtained in the subtraction process to positive values. Thus, the image resulting from the subtraction may be rectified, which provides the advantage that the frequency of the rectified pattern is double that of the carrier (i.e. the spatial frequency of the first interference fringe pattern). This property improves the discrimination of the moirxc3xa9 fringe pattern over the carrier compared with alternative processing techniques, such as addition where the carrier frequency is preserved. The further image will, of course, in general include the moirxc3xa9 fringe pattern and a finer pattern at, or close to, the carrier frequency.
The method may further comprise the steps of arranging the interferometer to form a third interference fringe pattern;
recording an image of the third interference fringe pattern;
arranging the interferometer to form a fourth interference fringe pattern;
recording an image of the fourth interference fringe pattern, wherein the first, third and fourth interference fringe patterns are phase shifted from each other by predetermined amounts; and
combining the image of the second interference fringe pattern with each of the recorded images of the first, third and fourth interference fringe patterns to produce respective said further images; and
processing the further images to produce a phase map of the perturbation of the optical path.
Thus, at least three phase-stepped xe2x80x9creferencexe2x80x9d interferograms may be generated and recorded, and combined with the second interference fringe pattern, i.e. the test interferogram, to produce respective further images.
The phase shifting or stepping may be achieved by conventional means (for example the use of piezoelectric transducer-driven mirrors).
Advantageously, the image of the second (test) interference fringe pattern may be an image selected from a recorded sequence of images of the interference pattern formed by the interferometer.
Thus, the changing interference pattern during a test may be recorded in real time, and then analysed at a later time by processing with the at least three phase stepped reference images to produce a full phase map of the perturbation at any given time in the measurement process.
Advantageously, the images of both the first and second patterns may be images selected from a recorded sequence of images of the interference pattern formed by the interferometer. Thus, the resultant moirxc3xa9 fringe pattern in the further image is indicative of only the changes in the interferometer arrangement between the two selected times.
Any two images (i.e. interferograms) may be selected from a recorded sequence and combined (e.g. digitally processed) to produce a resultant image comprising a moirxc3xa9 fringe pattern indicative of the change to the interferometer between the times at which the selected images were recorded.
Images of the interference fringe patterns formed by the interferometer may be captured and output as a continuous stream or sequence from an electronic camera. Each image may be combined with the stored first image to produce a respective further image and respective moirxc3xa9 fringe pattern which may be displayed in real time, e.g. at video rate.
According to a second aspect of the present invention there is provided measurement apparatus comprising:
an interferometer arranged to form interference fringe patterns comprising at least ten interference fringes;
a camera arranged to capture images of the interference fringe patterns;
an image store arranged to store an image of the interference fringe pattern captured by the camera at a selected time;
an image processor arranged to combine the stored image with an image of the interference fringe pattern captured by the camera at a different time to produce a further image comprising a moirxc3xa9 fringe pattern arising from a difference or differences between the interference fringe patterns at the selected and said different time.
The interferometer may, for example, be a Michelson interferometer, a Mach-Zehnder interferometer (as shown in FIG. 10) or may be based on an adapted xe2x80x9cSchlierenxe2x80x9d optical arrangement.
The interferometer may be arranged to form interference fringe patterns comprising at least fifty interference fringes, and the images may be digital images.
The image processor may be arranged to produce the further image by a process including at least the subtraction of one of the digital images from the other.
Additional processing may be performed on the images, such as filtering or normalisation of intensity distributions. This further processing may be performed on the images before, during, or after their combination to produce the further image including a moirxc3xa9 fringe pattern.
The further image or images may also be processed, for example by filtering to remove the underlying carrier fringe pattern and so leave only the moirxc3xa9 fringe pattern.
The image processor may be arranged to produce the further image by a process including the conversion of negative values obtained in the subtraction process to positive values, i.e. the processor may be arranged to rectify the intensity distribution calculated by subtraction.
The interferometer may include means for phase shifting the interference fringe patterns by predetermined amounts, the image store may be arranged to store images of the interference fringe patterns captured by the camera at at least three different selected times, the image processor may be arranged to combine each stored image with the image captured at a different time to produce a respective further image comprising a respective moirxc3xa9 fringe pattern, and the image processor may be further arranged to process the further images to produce a phase map. This phase map may be indicative of the perturbation to the interferometer between the different time and the time of capture of one of the stored images.
The camera may be arranged to output a continuous sequence of captured images of the interference fringe pattern, and the image processor may be arranged to combine the or one of the stored images with each one of the sequence of captured images and to produce a respective further image, which may be stored. The apparatus may further comprise a display for displaying the sequence of further images, and each further image may be displayed substantially as soon as it is produced. The sequence of further images may be displayed and/or stored at the same rate as the capture of images by the camera.
The measurement apparatus may further comprise an image recorder for recording the images captured by the camera, and an image selector for selecting one of the recorded images to be used as the stored image or the image to be combined with the stored image. Alternatively, both images may have been selected from a sequence of recorded images.
The camera may be a CCD camera to provide high resolution and fast response.
Advantageously, the interferometer may have an aperture of at least 10 cm. The aperture may be as large as 1 m, or larger still, as the further image production process inherently rejects the underlying imperfections in the interferometer components.
The advantage of subtracting one image from another (i.e. subtracting one intensity distribution from another) is that wherever the images are the same (the intensities are the same) the resultant image will show a dark region.
Generally, increasing the number of fringes in the first interference fringe pattern (i.e. the reference interferogram) increases the detail on the resultant moirxc3xa9 fringe pattern and improves the resolution of the perturbation to the interferometer. However, an upper limit to the density of the fringes (i.e. the maximum spatial frequency of the fringes in the recorded image of either the first interference fringe pattern or the second (test) pattern) is set by the resolution of the means used to record the image, for example the resolution or pixel density of the camera used to capture the image and the capacity of the image snore used to hold the recorded image.